Solar-Supercapacitor Harvesting System Design for

Energy-Aware Applications

Moeen Hassanalieragh, Tolga Soyata, Andrew Nadeau, Gaurav Sharma

University of Rochester, Dept. of Electrical and Computer Engineering, Rochester, NY 14627 { m.hassanalieragh,tolga.soyata,andrew.nadeau,gaurav.sharma} @rochester.edu

Abstract-Supercapacitors are an emerging choice for energy buffering in field systems and their use in solar-powered field systems has been the focus of recent research. Supercapacitors offer advantages compared to rechargeable batteries for energy buffering due to their energy charge/discharge efficiency as well as environmental friendliness. Additionally, a supercapacitor­based system permits an energy-aware operation due to its superior energy-predictability. This paper describes a circuit for solar/supercapacitor energy harvesting, which includes power and voltage measurements, voltage regulation circuit and RS232 communication capability with the host embedded processor. A complete system is prototyped and its operation is discussed in terms of design parameters.

I. INTRODUCTION

Recent research focused on powering Wireless Sensor Net­

works [1] and field systems using supercapacitors [2] due to

their potential in providing a battery less power supply for

embedded systems, thereby yielding a much longer opera­

tional lifetime. Although these two type of systems do not

take advantage of one of the most important high power

density feature of supercapacitors, which is the backbone of

other high-powered applications such as industrial elevators or

electric vehicles [3]-[5], another equally important feature of

the supercapacitors are taken advantage of by both of these

applications : energy efficiency and their superior energy pre­

dictability by observing the supercapacitor terminal voltage,

Vse and predicting the remaining energy as E= �CVs�. Although a rich body of circuit references exist for the

building blocks of an energy harvesting system, a complete

harvesting system design for incorporating energy awareness

into higher system levels is not readily available which details

relevant design and runtime issues. In this paper, we intro­

duce a microcontroller-based energy harvester design which

receives its energy from multiple solar panels, harvests energy

by using a DC-DC converter and stores the harvested energy

in two blocks of supercapacitor. This battery-less harvester is

intended to power field systems with an embedded CPU, such

as Nexus 7, with a target overall system power consumption

of 0.5-10 W. We demonstrate results on a prototype we built,

shown in Figure 1.

The primary goal of our design is to create a solar harvesting

platform that not only buffers energy to sustain operation,

but provides the embedded processor with enough information

to make intelligent decisions to take advantage of remaining

energy. We detail multiple design issues relevant to such a

field system harvester and elaborate on each issue.

Fig. 1. Our prototype solar/supercapacitor harvesting system along with supercapacitor reservoirs and the embedded processor.

This paper is organized as follows: In Section II, we provide

background information on solar panels and supercapacitors.

Section III is where we introduce our proposed system,

in Section IV details of the harvesting circuit is presented

followed by evaluations on our prototype in Section V. We

draw conclusions in Section VI.

II. BACKGROUND AND RELATED WORK

A. Solar Energy

In recent years photovoltaic (PV) cells have gained much

interest to increase the autonomy of embedded systems. The output characteristics of a PV cell varies non-linearly with en­

vironmental conditions such as temperature and irradiation [6],

[7]. Also, the power gained from a PV cell greatly depends

on its operating point, i.e we need to keep it at its optimum

operating point by demanding sufficient amount of energy.

When the demanded current from a PV cell is high, its terminal

voltage drops to a very small value. This current is denoted

by the short circuit current ISolaT = Ise. When there is no

current demand from the PV cell, its terminal voltage increases

to the open circuit voltage. At both of these extreme cases no

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Oam 6am Noon 6pm Oam

A mixed weather day (US East)

Oam 6am Noon 6pm Oam

A sunny day (Italy)

Oam 6am Noon 6pm Oam

A cloudy day (Italy) ,..----------..,28.4 2'

� 21.3 e-

� a.

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Fig. 2. Example solar power levels under varying weather conditions. Results in Italy obtained from [6]

power is generated by the PV cell. Thus, there is a need for

an algorithm which keeps the PV cell at its maximum power

point (MPP). These methods are called maximum power

point tracking (MPPT) methods. Several MPPT methods have

already been proposed [8], [9]. These methods differ in their

means of implementation. Based on their level of complexity,

some of them need a digital processor to be implemented while

the others can be realized using analog components.

We provide solar power into our system using Radio Shack

Model 277052 solar panels. These panels have a 6 V output

voltage and can provide 1.5 W of output power, as per speci­

fications. Having a hybrid architecture of them in parallel and

series could yield to desirable operating voltage and power

to provide power for a variety of compute-intensive field

applications [10], [11].

The harvested power is almost linearly dependent on the

solar irradiation levels [12], measured in KLux (Kilo Lu­

mens per m2). From measurements, we determined that, the

specified 1.5 W solar power for the Radio Shack panels are

reached at a 200 KLux sunlight. This is achieved on a very

sunny day under bright sunshine. Solar energy patterns for

different weather conditions are shown in Figure 2 for a block

of 21 panels, organized as a 7 x 3 grid. Figure 2 depicts

the dependence of solar power output on sunshine patterns.

A small cloud block can reduce the solar intensity from

200 KLux to 40 KLux almost instantenously. Our experiments

in US East are shown to yield similar patterns to studies in

Italy [6]. This emphasizes that, a solar harvesting system must

employ an MPPT algorithm by tracking the sunlight patterns

continuously to provide efficient results [1].

B. Supercapacitors

Supercapacitors store energy based on two phenomena

occurring at the electrode-electrolyte interface: a) EDL (elec­

tric double layer) and b) pseudocapacitance. EDL allows

supercapacitors to store energy by layers of charged ions

from the electrolyte attracted to the electrode surface by

electrostatic forces or selective adsorption of ions into the

surface, whereas Pseudocapacitance allows supercapacitors

to store energy chemically, similar to batteries [13]. Compared

to conventional capacitors, supercapacitors have significantly

different operational characteristics which must be considered

when a system is designed with them [14]-[16].

Figure 3 shows a set of eight Maxwell 3000 F superca­

pacitors [17] connected in series, with individual maximum

Fig. 3. Energy buffer: 8 series Maxwell BCAP3000 supercapacitors [17] .

voltages of 2.7 V and a combined supercapacitor block voltage

of 21.6V A total energy of E = � x 3000 X 2.72 = 109351 is stored in each supercapacitor, with a combined storage of

878401 total for a block of eight supercapacitors. Note that,

this energy estimation can yield erroneous results in certain

conditions due to charge redistribution [18]. Due to their

capability to store such a high amount of energy, extreme care

must be taken to prevent short-circuiting them.

III. SOLAR ENERGY HARVESTING SYSTEM DESIGN

Figure 4 shows the overall system architecture. Solar energy

is buffered on two supercapacitor reservoirs using an energy

harvesting circuit. Primary reservoir is intended to power up

the embedded processor. Secondary reservoir has the role of

supplying energy for the microcontroller that is the crucial

part in our energy harvesting circuit. Energy transfer from

reservoirs to microcontroller and the embedded processor is

realized using two DC-DC converters.

A. Nexus 7 Tablet - Embedded Processor

Data processing in the field requires substantial computa­

tional capability that urges us to use an embedded processor.

We have selected Google Nexus 7 tablet which contains Tegra3

quad-core mobile processor. Nexus 7 power consumption

varies between 0.5-6 W , based on its frequency and number

of active cores. Having extra peripherals attached to Nexus

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Solar

Energy

Energy

Harvesting

Circuit

n Re�e

a:oir _I

n 5 Volt

Regulator

Auxiliary Reservoir

=>I=> 5 Volt

Regulator

L n

Micro Controller & Peripherals Circuit

=> J Fig. 4. Architectural diagram of the harvesting system.

7 could lead to a maximum power consumption of 10 W at

5 V. Nexus 7 power proportionality makes it an ideal choice

for field systems that need to adapt the processing power

consumption based on the available energy.

B. Microcontroller Selection

The microcontroller suitable for our application should

include the following features: 1) 1/0 pins to control the

MOSFETs. 2) Having an I/O voltage of at least 5 V in order

to be able to turn onloff the MOSFETs. 3) Multiple ADC

channels to sample the voltage on different nodes (both differ­

ential and single ended). 4) a UART module for transferring

information through the RS232 port. The 8-bit PICI6F1783

microcontroller satisfies all of these conditions, and contains

an internal voltage reference of 4096 m V. An industry standard

TTL to RS232 converter ADM232LAN allows connection to

a standard RS-232 port, and a gate driver MAX627 is used

to drive power MOSFETs directly from PIC 1/0 pins. The

current sense amplifier is MAX4372H allows us to convert 1-

2000 mA current levels to PIC-readable voltage levels, upto

4096 m V. Total power consumption of the microcontroller and

its peripherals does not exceed 250 m W.

C. Dual-Reservoir Architecture

Our system consists of two reservoirs for buffering the

harvested energy: The Main Reservoir and the Auxiliary

Reservoir are constructed from 8x(3000 F, 2.7 V) and 9x(50 F,

2.7 V) supercapacitors. The Main reservoir provides power to

the Nexus 7 tablet, while the Auxiliary reservoir powers the

microcontroller and its perhiherals. Having a separate reservoir

for the microcontroller ensures that, in case of a complete

depletion of the Main Reservoir, the microcontroller and its

peripherals could be brought back in operational mode quickly,

thereby eliminating the possibility of a deadlocked operational

mode.

Energy is channelled to these separate reservoirs through

a software switch. Having a wide voltage range on the main

reservoir is crucial to take advantage of the maximum available

energy in the supercapacitors. Based on Nexus 7 power

specifications, we chose LTC1624 as the switching regulator,

z � C III I (J) C

VNEXUS2 100kQ NEXUS5V

GNO

GNO

Fig. S. Nexus 7 Voltage Regulator, input=(3.S-21.6 V) , Output=S V, 2 A

PICVOO

GNO

1N4148 + hGNO¢. 100llF

+ T

100llF �GNO

1nF

Fig. 6. /.lC Voltage Regulator, input=(S.S-24.3 V) , Output=S V, 2S0 rnA

configured in SEPIC mode. Its input voltage range is 3.5-36 V,

which completely suits our application. Since this regulator

uses an external MOSFET switch, we can provide sufficient

power to Nexus 7 via a power MOSFET. Use of this regulator

eliminates the need of a gate driver to drive the switch, since it

has an internal one. We can see the configuration in Figure 5.

This regulator has also the capability to shut down when

needed by setting its RUN pin to GND (pin 2). This pin

is controlled by the PIC software (Nexus_SD pin) through

the 2N7002 transistor. Based on the microcontroller power

requirement, we chose ADP3050-5 which is a 5 V, 1 A Buck

regulator with an internal switch. The configuration is depicted

in Figure 6. Using a Buck regulator imposes the constraint

that voltage on the auxiliary reservoir should not go below

5.5 V for proper operation. 5 V generated by this regulator

also feeds the Boost pin of Nexus regulator thorough a diode.

Boost pin actually supplies the voltage of the internal gate

driver of LTC 1624. This regulator has an internal 5 V generator

for providing the boost voltage, but it only works when the

input voltage to the regulator is higher than 5 V. Externally

connected 5 V insures proper operation for voltage range of

3.5-5 V. This block provides sufficient power to a host system

running sophisticated energy-aware algorithms [19]-[21].

282

VSolar_Sense

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Tl00nF

�GND

100�H

100�H

GND

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GND Fig. 7. Solar Energy Harvesting Circuit built around a SEPlC DC-DC converter

IV. ENERGY HARVESTING CIRCUIT

An energy harvesting circuit is essential to deliver the avail­

able input solar energy to supercapacitors. DC-DC converters

are a specific type of energy transfer circuits that adjust the

amount of energy taken from the input in order to keep their

output voltage level at a certain value. It is essential to notice

that in the harvesting platform we do not intend to go from one

voltage level to another, but keep the input solar panels voltage

at the optimum point and transfer the harvested energy to

reservoirs. We will go through the harvesting circuit elements

in detail in following subsections.

A. SEPIC DC-DC Converter

In this paper we have used a special class of DC-DC

converters as the energy transfer mechanism. While the most

commonly used DC-DC converter designs are Buck, Boost, or

Buck-Boost [22], our experiments show that, a less common

design, SEPIC Converter [23] is lot more suitable due to the

following reasons:

1) While Buck and Boost designs can only up-convert and

down-convert, respectively [22], SEPIC can be used as

the energy transfer element in a variety of input - output

voltage ranges.

2) SEPIC has a continuous-input current and

discontinuous-output current draw [23]. With proper

electrolytic capacitors on the output side of the

system, capacity losses at the supercapacitors at high

frequencies [24] can be eliminated. Therefore, SEPIC is

a reasonably efficient solution for a an energy transfer

circuit that is providing current into a supercapacitor.

3) SEPIC provides a graceful short-circuit response [23]

which is important for field systems working in harsh

environments.

Figure 7 shows the harvesting circuit. As mentioned in

section II, we need to keep the solar panel input power at

the optimum point in order to absorb the maximum power.

In SEPIC configuration this is achieved by adjusting the duty

cycle of the switch based on the feedback from measuring

the voltage of the solar panel. As the duty cycle of the

switch control signal increases, the leftmost inductor in SEPIC

configuration is turned on more percentage of time and this

means increased average current demand from the solar panel

and vice versa. Thus, we can move in I-V curve of the solar

panel by adjusting the duty cycle of the switch signal. This

signal is denoted by IRF _Gate in Figure 7 which is generated

by the microcontroller.

B. Microcontroller Software

An important issue in solar harvesting platforms is finding

the maximum power point of the solar panel. The micro­

controller software is responsible for this task. We used a

periodic calibration technique in which the system tries to

find the new optimum point by searching the points in a

region around the current optimum point in fixed intervals. The

optimum point is simply found by sampling the input current

and voltage in search space and find the one with maximum

product. This algorithm is less prone to getting stuck in local

maxima compared to gradient descent algorithms if the search

space is large enough around the current optimum point. The

calibration period is chosen to be five minutes based on the

fact the rate of change in environmental conditions such as

light intensity, temperature, etc. is not very high. The value

of input capacitance in SEPIC plays an important role in our

search based algorithm. The higher its value the slower the

change is in input I-V curve. It must be high enough so that the

microcontroller ADC sampling rate yields to sufficient search

points for finding the optimum point.

e. Power MOSFET Selection and Gate Driver

The transistor switch in the SEPIC converter plays an

important role in the harvesting circuit functionality and its

efficiency. When choosing a transistor switch several parame­

ters must be taken into account. The threshold voltage, ON

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resistance, maximum drain source voltage in off state and

overall gate charge. In SEPIC configuration there can be a

maximum voltage of Yin + Vout over the transistor at the off

state, so this should be strictly taken into consideration. ON

resistance of the switch has a substantial effect on efficiency

of the circuit. ON resistance is dependent on the gate source

voltage with which the transistor is driven. Overall gate charge

of the transistor determines how long it takes for the transistor

to change state from ON to OFF and vice versa. During this

transition, transistor is consuming a considerable amount of

energy. In order to provide the gate charge in a smaller amount

of time, use of a gate driver is crucial. As shown in Figure 7,

MAX627 is used as the gate driver to drive the SEPIC switch.

D. Current Sensing

Current sensing is of high importance in harvesting circuits

for determining the maximum power point. Basically current

sensing is done through measuring the difference voltage

across a small resistor which is called the sense resistor.

Conventional values for sense resistors range from 5-100 mfl for decreasing power loss on the sense part. Since voltage drop

on the sense resistor would be so small, we used a current

sense amplifier for amplifying this voltage and then feeding it

to ADC of the microcontroller.

An important factor for choosing a current sense amplifier is

where the sense resistor is actually placed in the circuit. Sense

resistor can be placed either right after the input source (high

side sensing) or on the load part (low side sensing). In high

side sensing configuration, the current sense amplifier will face

a high common mode voltage that must be considered when

choosing a current sense amplifier. Based on our requirements,

we chose MAX4372H which is a high side current sense

amplifier with a gain of 100. Current sense amplifiers are

designed to measure DC current so their effective bandwidth

is not high. This must be taken into account when measuring

fast varying currents. Output of the current sense amplifier is

denoted by ISolar in Figure 7. The value of the sense resistor

must be chosen in a way that the current sense amplifier's

output will not exceed the maximum sampling voltage of the

ADC. We did not use a current sense amplifier for sensing

the outgoing current to Nexus 7. As shown in Figure 5, the

difference voltage across the sense resistor is directly sampled

by microcontroller's differential ADC since they do not have

a high common voltage.

V. EVALUATION

A. Efficiency Analysis

Power consumption in the harvesting circuit mostly consists

of two parts. The first one is the quiescent current of the

present integrated circuits and the other one is due to energy

loss in circuit components such as transistors and inductors.

The first term manifests in the form of constant current loss, so

the power consumption will be higher when the input voltage

increases.

The harvesting efficiency was determined by measuring the

input solar power and the average power harvested on the

auxiliary reservOir In a certain amount of time. We chose

the auxiliary reservoir for the measurement since it feeds

the microcontroller regulation circuit. The experiment was

conducted in a wide range of input solar power. The results

are shown in Table I. At low solar power input, the quiescent

power consumption causes the efficiency to drop. At high solar

power input, the circuit components loss (especially the SEPIC

switch) dominates and causes the efficiency to decrease.

Input Power (W) Efficiency (%) 1.4 77.2 5.6 80.6 7 84.2

9.8 78.3 12.6 75.6 18.2 75.1 21 74.3

23.8 72.6

TABLE I MEASURED HARVESTING EFFICIENCY AT DIFFERENT SOLAR POWERS

B. Supercapacitor Energy Estimation

Measuring the remaining energy in a supercapacitor using

the formula �CVs� holds true when it is in a stable condition.

Supercapacitors differ from conventional capacitors in a way

that they consist of multiple resistance-capacitance branches

with different time constants [16]. Measurements are valid

only when all of the branches have reached a stable condition

and no charge distribution is happening between branches.

Thus, if we intend to compute the remaining energy by

observing the terminal voltage in non-stable scenarios, we

should keep track of branches state of charge. Recently a

Kalman filtering approach is introduced to track and estimate

the remaining energy in a supercapacitor by observing its

terminal voltage and the total current flowing through the

supercapacitor [18].

C. Supercapacitor Overcharging Consideration

Experiments we conducted on multiple supercapacitors

showed manufacturing tolerances ranging from 2855 F to

3139 F for Maxwell 3000 F supercapacitors [17]. Although the

average is almost a perfect 3039 F, there is a subtle problem. If

the block of eight supercapacitors are operated at 21.6 V, the

same current flowing through them will charge the smallest

supercapacitor to a higher voltage, thereby yielding a 2.87 V

on the smallest (i.e., 2855 F), and a 2.61 V on the largest

supercapacitor (i.e., 3139 F). In other words, while the smallest

supercapacitor is overcharged, the largest one is underchanged.

While sophisticated circuit techniques can be employed to in­

dividually control the supercapacitor voltages in the block, the

simplest solution is to limit the supercapacitor block voltage

(Vsc) to a Vscmax<21.6 V, where the smallest supercapacitor

stays below 2.7 V. This ends up being VSCmax = 20.3 V.

D. Connection to Nexus 7

Nexus 7 tablet primarily uses an internal Li-Ion battery. In

order to power up the tablet using the custom regulator, we had

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to remove the battery and manually connect the supply pins.

Li-Ion battery block has extra connections which report state

of charge of the battery to the hardware. The lack of existence

of these connections caused the operating system to assume

that the battery is out of power and it automatically turned

off the power to the USB port. The USB port is connected to

RS232 connection of the microcontroller through USB-RS232

converter. We connected the 5 V feeding the tablet directly to

supply pins of the USB port to solve the problem.

VI. CONCLUSIONS AND FUTURE W ORK

This paper introduces a SEPIC-based solar energy harvester,

which buffers the harvested energy in two supercapacitor

blocks. Our proof-of-concept circuit is capable of harvesting

solar energy from 18 solar panels (a total of 24 W at 200 KLux

solar intensity). The harvested solar energy is intended to

power up an embedded processor for conducting data-intensive

field processing. Continuous power measurements inside the

circuit and reporting it to the embedded processor allows the

software to make energy-aware decisions.

Although the main reservoir block can theoretically store

;::::: 88KJ energy, in practice, we found a batch of Maxwell

3000 F supercapacitors to have values in the 2855 F to 3139 F

range. This implies overcharging on the smallest one, if the

block of eight supercapacitors are charged to 8 x 2.7= 21.6 V. Therefore, we suggest the simplest method of keeping the

block voltage at 20.3 V which will eliminate the overcharging

issue, albeit at the expense of leaving unused energy in

the block. Another solution to overcharging is the parallel

supercapacitor configuration, which we leave as future work.

ACKNOWLEDGMENT

This work was supported in part by the National Science

Foundation grant CNS-1239423 and a gift from Nvidia Corp.

REFERENCES

[1] Davide Brunelli, Luca Benini. Clemens Moser, and Lothar Thiele, "An efficient solar energy harvester for wireless sensor nodes," in Con! on Design, Automation and Test in Europe (DATE), Munich, Germany, Mar. 2008, pp. 104-109.

[2] Amal Fahad, Tolga Soyata, Tai Wang, Gaurav Sharma, Wendi Heinzel­man, and Kai Shen, "SOLARCAP: super capacitor buffering of solar energy for self-sustainable field systems," in Proceedings of the 25th IEEE International System-on-Chip Conference, Niagara Falls, NY, Sep 2012, pp. 236-241.

[3] N. Jinrui, W. Zhifu, and R. Qinglian, "Simulation and Analysis of Performance of a Pure Electric Vehicle with a Super-capacitor," in IEEE Vehicle Power and Propulsion Conference, 2006, pp. 1-6.

[4] H. Zhang, Y. Sun, S. Ding, and Y. Wang, "Application of super capacitor with full-digital converter in hybrid electric vehicle energy transmission system," in 27th Chinese Control Coriference, 2008, pp. 212-215.

[5] Alfred Rufer and Philippe Barrade, "A supercapacitor-based energy storage system for elevators with soft com mutated interface," IEEE Transactions on Industry Applications, vol. 38, no. 5, pp. 1151-1159, 2002.

[6] Roberto Faranda and Sonia Leva, "Energy comparison of mppt tech­niques for pv systems," WSEAS Transactions on Power Systems, vol. 3, no. 6, pp. 446-455, 2008.

[7] Davide Brunelli, Clemens Moser, Lothar Thiele, and Luca Benini, "Design of a solar-harvesting circuit for battery less embedded systems," Circuits and Systems 1: Regular Papers, IEEE Transactions on, vol. 56, no. 11, pp. 2519-2528, 2009.

[8] D.P.Hohm and M.E.Ropp, "Comparative study of maximum power point tracking algorithms using an experimental, programmable, maximum power point tracking test bed," in Proc. Photovoltaic Specialist Confer­ence, 2000, pp. 1699-1702.

[9] D.S. Hyun D.Y. Lee, H.J. Noh and l.Choy, "An improved mppt converter using current compensation method for small scaled pvapplications," in Proc. APEC, 2003, pp. 540-545.

[l0] Tolga Soyata, He Ba, Wendi Heinzelman, Minseok Kwon, and Jiye Shi, "Accelerating mobile cloud computing: A survey," in Communication Irifrastructures for Cloud Computing, H. T. Mouftah and B. Kantarci, Eds., chapter 8, pp. 175-197. IGl Global, Hershey, PA, USA, Sep 2013.

[11] Tolga Soyata, Rajani Muraleedharan, Colin Funai, Minseok Kwon, and Wendi Heinzelman, "Cloud-Vision: Real-Time face recognition using a Mobile-Cloudlet-Cloud acceleration architecture," in Proceedings of the 17th IEEE Symposium on Computers and Communications (IEEE ISCC

2012), Cappadocia, Turkey, Jul 2012, pp. 59-66. [l2] Dave Freeman, "Introduction to Photovoltaic Systems Maximum Power

Point Tracking," http://www.ti.comllitian/slva446/slva446.pdf, 2010. [l3] B.E. Conway, Y. Birss, and J. Wojtowicz, "The role and utilization of

pseudocapacitance for energy storage by supercapacitors," Journal of Power Sources, vol. 66, no. 12, pp. 1 - 14, 1997.

[l4] Jianjun Niu, Wendy G. Pelt, and Brian E. Conway, "Requirements for performance characterization of c double-layer supercapacitors: Applications to a high specific-area c-c1oth material," fournal of Power

Sources, vol. 156, no. 2, pp. 725 - 740, 2006. [15] S. Buller, E. Karden, D. Kok, and R.W. De Doncker, "Modeling the

dynamic behavior of supercapacitors using impedance spectroscopy," in Industry Applications Conference, 2001. Thirty-Sixth lAS Annual Meeting. Conference Record of the 2001 IEEE, 2001, vol. 4, pp. 2500-2504 vol.4.

[l6] L. Zubieta and Richard Bonert, "Characterization of double-layer capacitors for power electronics applications," Industry Applications, IEEE Transactions on, vol. 36, no. 1, pp. 199-205, 2000.

[17] Maxwell Corp., "K2 Series High Capacity Cells," http://www.maxwell. comlproducts/ultracapacitors/products/k2-series, 2012.

[l8] Andrew Nadeau, Gaurav Sharma, and Tolga Soyata, "State-of-charge estimation for supercapacitors: A kalman filtering formulation," in Proceedings of the 2014 IEEE International Coriference on Acoustics, Speech and Signal Processing (ICASSP 2013), Florence, Italy, May 2014, pp. 2213-2217.

[19] Tolga Soyata and Eby G. Friedman, "Retiming with non-zero clock skew, variable register and interconnect delay," in Proceedings of the IEEE Conference on Computer-Aided Design, Nov 1994, pp. 234-241.

[20] Tolga Soyata and Eby G. Friedman, "Synchronous performance and reliability improvements in pipelined asics," in Proceedings of the IEEE

ASIC Coriference, Sep 1994, pp. 383-390. [21] Tolga Soyata, Eby G. Friedman, and J. H. Mulligan, "Integration of

clock skew and register delays into a retiming algorithm," in Proceedings

of the International Symposium on Circuits and Systems, May 1993, pp. 1483-1486.

[22] Abraham Pressman, Keith Billings, and Taylor Morey, Switching Power Supply Design, Mc Graw-HiII, 2009.

[23] Texas Instruments Incorporated, "Designing DCIDC converters based on SEPIC technology," http://www.ti.com/litian/slyt309/slyt309.pdf. 2013.

[24] Maxwell Corp., "Maxwell BOOSTCAP Product Guide," http://www.maxwell.com/products/ultracapacitors/docs/ 1 0 14627\_ boostcap\_product\_guide.pdf, 2013.

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